"This incident is [in line with] repeated attempts by Algeria and Polisario aimed at scuttling UN efforts to relaunch the dynamic of [peace] negotiations," the statement said.
The ministry urged action by the United Nations to "assume responsibility and take the required actions."
Mansour Omar, a representative of the Polisario Front in France, told Al Jazeera that Morocco's claims were overblown.
"A group of people of various nationalities; Sahrawis, Spanish, French and Latin Americans, are used to demonstrating every year in front of the [security] 'belt' set by Morocco in the Western Sahara, not in Moroccan territories," he said.
"It was a peaceful demonstration which they stage every year. What is new is that Morocco may have exaggerated.
"The demonstration was staged in 'the free zone of the Sahrawi Arab republic', not in Morocco," he said.
It is the first time in years that Rabat has linked Algiers directly to an alleged violation of the ceasefire deal between the Polisario Front and Morocco, diplomats say.
While the Moroccan government wants Western Sahara to be an autonomous region of Morocco, Polisario is looking to have a referendum on the territory's independence.